Math [Probability]

I'm in a Grade 12 Data Management Course. The Current unit is Factorials and Permutations. I'm having a trouble with this question. The answer is suppose to be 120 but I don't know how.

How many different ways can 6 people be seated at a round table? Explain your reasoning.

If they were being placed on a line then there would be 6! ways to arrange them. But since they're being seated in a circle up to symmetry there are only (n-1)! or 5! different ways to arrange them. Try arranging 4 items in a circle and see how many unique ways there are, with respect to the objects.
If the chairs were labeled somehow, then there would be 6! ways.
I should point out that the question is slightly ambiguous. You might want to point this out in class.

Thanks for the help, Roger. I'll be sure to let me teacher know this in class, but there's still something I don't understand. I know they're being seated in a circle, but what do you mean by 'up to symmetry'?

That means the number of unique positions before they're equivalent in some sense.
If you take any arrangement you should see that any of 6 possible starting positions could be used. After one is chosen, all the rest are symmetrical. If you rotated the circle then it would be a different view, but not a different arrangement. If you do this for 3 or 4 objects you should see what I mean.

the question is The indianapolis motor speedway has 3,200,000 bricks that lie beneath the 2.5 miles of track.find how many bricks lie under one mile of track at the race track

Would that be 3,200,000 divided by 2.5?

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  1. a die is rolled and the spinner is spun. Find the probability

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  2. 78125 bricks

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